Second order Integral Sliding Mode Control: an approach to speed control of DC Motor

Abstract

In this paper, a second order sliding mode controller is applied for single-input single-output (SISO) uncertain system. The presented controller successively overcomes the variations caused by the uncertainties and external load disturbances although an approximate model of the system is used in the design procedure. An integral type sliding surface is used and the stability and robustness properties of the controller are proved by means of Lyapunov stability theorem. The chattering phenomenon is significantly reduced adopting the switching gain with the known parameters of the system. Thus, the presented controller is suitable for long-term application to the systems those are having fast response closed-loop behaviours. The performance of the developed control scheme is validated by simulation in Mathworks MATLAB and the results are compared with the similar controllers presented in the literature. In order to verify the performance comparison of second order integral sliding mode approach, first, a sliding mode control system with a PID sliding surface is adopted to control the speed of an electromechanical plant. In this, a sliding mode controller Is derived so that the actual trajectory tracks the desired trajectory despite uncertainty, nonlinear dynamics, and external disturbances. The sliding mode controller is chosen to ensure the stability of overall dynamics during the reaching phase and sliding phase. The stability of the system is guaranteed in the sense of the Lyapunov stability theorem. Second, the sliding mode approach for stable systems which is available in the literature is designed with tuning parameters as per their guidelines. And finally conventional controller is designed based on the Zeiglar-Nicholas approach. All controllers applied to the electro-mechanical system to verify the performance in terms of time domain and performance error indices. The chattering problem is almost removed in the presented approach in comparison with other controllers. This problem is overcome using a hyperbolic function in the switching control considering the small constant term incase of the zero error to avoid the problem of zero division.